In the AP (-47,-31,-15,\ldots), what is the first term greater than (500)?
Answer and explanation
Correct answer: 513
Here, the first term is \(a=-47\) and the common difference is \(d=16\). Thus, \(a_n=-47+16(n-1)=16n-63\). For \(a_n>500\), \(16n-63>500\), so \(n>35.1875\). The smallest integer value is \(n=36\), giving \(a_{36}=513\). Option 497 is not greater than 500. Exam tip: For “greater than,” use the next integer term satisfying the inequality.
Frequently asked questions
What is the correct answer to this question?
513
Why is this the correct answer?
Here, the first term is \(a=-47\) and the common difference is \(d=16\). Thus, \(a_n=-47+16(n-1)=16n-63\). For \(a_n>500\), \(16n-63>500\), so \(n>35.1875\). The smallest integer value is \(n=36\), giving \(a_{36}=513\). Option 497 is not greater than 500. Exam tip: For “greater than,” use the next integer term satisfying the inequality.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the $n$th term of an AP.
